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Let $C$ be the intersection of $x^2{y}^2=16$ and $xyz=5.$

Find the curvature of $C$ at $(0,4,1).$

$\frac{\sqrt[\phantom{2}]{3}}{16}$

$\frac{\sqrt[\phantom{2}]{6}}{16}$

$\frac{\sqrt[\phantom{2}]{6}}{15}$

$\frac{\sqrt[\phantom{2}]{2}}{16}$